# Stress, Strain, Viscoelastic behavior

Stress or load: Force over area (has units of Newton per square metre)

Strain or deformation: Change in length over original length caused by applied stress or load (unitless and expressed as ratio or percentage)

Mnemonic: If your boss is under a lot of stress, his personality changes (strain)

A. Elastic zone: The molecular bonds are stretched but not broken

• A = Proportional limit: Point upto which Hook’s law (Stress is directly proportional to strain) is obeyed
• Young’s modulus of elasticity = Stress/Strain (Higher modulus = Steeper curve = Stiffer material)
• B = Elastic limit: Point at which deformation stops being entirely reversible

B. B-C: Yield stress – stress needed to induce a specified amount of permanent strain, typically 0.2%

• C = Yield point: Point at which the material starts to undergo plastic deformation

C. Plastic zone:

• C-D = Ultimate stress: Maximum stress that the material has to bear before break or failure
• Yielding:  Once, the yield point is passed, the material will undergo considerable elongation (yielding) with little or no increase in stress (flat part of curve)
• Strain hardening: the plastic deformation increases a materialâ€™s resistance to further deformation due to the material undergoing changes in its atomic and crystalline structure
• D = Ultimate stress point
• D-E = Necking: Zone where stretching occurs with an actual reduction in the stress due to reduction in cross-sectional area

Toughness (Strain energy): Area under the stressâ€“strain curve represents the energy absorbed per unit volume of the material. It therefore indicates the energy absorbed by the material to failure. This is called toughness.

Stiffness: is defined as the slope of a force versus displacement graph.

Strength: is an imprecise term and represents the degree of resistance to deformation of a material. A material is strong if it has a high ultimate tensile strength.

Hardness: describes a materialâ€™s resistance to localized surface plastic deformation, e.g., scratch or dent.

Ductile: Large deformation between elastic point and breaking point (sees post-yield deformation)

Brittle: Small deformation between elastic point and breaking point (linear up to failure)

Fatigue failure: Failure of material by stress below ultimate tensile strength

Endurance limit: Stress below which unlimited cycles of load can be applied without failure

### Viscoelastic behavior

In a viscoelastic material, stress-strain behavior is time-rate dependent, i.e., they react differently when loads are exerted over different time periods. It relates to a materialâ€™s ability to adjust to that load given time. Characteristics of a viscoelastic material include –

1. Creep

• Applied stress or load is kept constant
• Progressive deformation of material is observed (deformation is permanent) over time

2. Stress relaxation

• Strain is kept constant
• Stress peaks and relaxes over time

3. Hysteresis

• The energy lost from the deformation since viscoelastic materials are not perfect elastic materials

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